Buy Multivariate Statistical Analysis Assignment
By Thursday, March 29, read Chapters 11–12 and 16 of Applied Multivariate Statistical Analysis,
fourth edition; by Wolfgang Härdle and Léopold Simar.
By Tuesday, April 3, read Chapter 14 of Härdle and Simar.
The following problems are nominally due on Thursday, April 5, but can also be submitted in
class on Tue or Thu, April 10 or 12, or to the course mailbox in Room 904 SSW, any time before
5:00pm on Friday, April 13.
1. A sample of n = 140 seventh-grade children received four tests on x1 = reading speed,
x2 = reading power, y1 = arithmetic speed, and y2 = arithmetic power. The correlations
for performance are
( RXX RXY
RY X RY Y
1.0000 0.6328 0.2412 0.0586
0.6328 1.0000 −0.0553 0.0655 0.2412 −0.0553 1.0000 0.4248 0.0586 0.0655 0.4248 1.0000
(a) Find the sample canonical correlation coefficients and sample canonical variables.
(b) Find the p-value for a test of H0 : ΣXY = 0.
(c) If you reject H0 : ρ1 = ρ2 = 0 at the α = .05 level of significance, find the p-value for
a test of H0 : ρ2 = 0.
(d) Does reading ability (as measured by the two tests) correlate with arithmetic ability
(as measured by the two tests)? Discuss.
2. A random sample of n = 70 families will be surveyed to determine the association between
certain “demographic” variables and certain “consumption” variables.
Define the Criterion set of variables by
y1 = annual frequency of dining at a restaurant
y2 = annual frequency of attending movies
and the Predictor set by
x1 = age of head of household
x2 = annual family income
x3 = educational level of head of household
Suppose 70 observations on the preceding variables give the sample correlation matrix
( RXX RXY
RY X RY Y
1.00 0.37 0.21 0.26 0.33
0.37 1.00 0.35 0.67 0.59
0.21 0.35 1.00 0.34 0.34
0.26 0.67 0.34 1.00 0.80
0.33 0.59 0.34 0.80 1.00
(a) Determine the sample canonical correlation coefficients, and find the p-value for a
test of the null hypothesis H0 : ΣXY = 0.
(b) If H0 : ΣXY = 0 is rejected at the α = .05 level, test the null hypothesis that the
second and higher canonical correlations are all zero.
(c) Using standardized variables, construct the canonical variables corresponding to the
significant (α = .05) canonical correlation(s).
(d) Interpret the canonical variates corresponding to significant (α = .05) canonical cor-
(e) Do the demographic variables have something to say about the consumption vari-
ables? Do the consumption variables provide information about the demographic